Through Darkest Peirce

Effect: "A card sharp, to be successful, must possess an exceptional memory and a clear mind. Not only must he remember all the cards he sees, he must follow their positions as they are shuffled and dealt into hands, and as they are picked up again. To complicate matters, the number of hands may vary as people leave or join the game. A magician has an advantage over a card sharp in this. Let me show you." The performer removes about a quarter of the deck and sets the rest aside. He gives the packet a shuffle or two, as he explains:

"To speed up the demonstration, I'll use only a few cards. If I were a sharper, I would have memorized their order. They are now randomly mixed; but the card shar p must follow them past this, as they are dealt out and gathered. Will someone suggest a number of hands?" A number is decided on and the packet is dealt face-down into that many hands. The hands are gathered and dealt out again into any number of hands called for by the audi-ence. This can be repeated as many times as desired, but two or three rounds usually satiate the average group's appetite for mixing.

"You will agree that the cards are well mixed. However, being a magician, I shall add to the challenge by having a card chosen. We'll take one by chance. This card on the top of the packet is a seven, so we'll choose the seventh card." The seventh card from the top of the packet is counted to and shown. It is an ace.

"Now we'll mix the cards with one more deal; say, five hands." The cards are dealt and gathered. "I told you earlier that a magician has his own way of following the order of the cards. He does so by making use of the sympathy that exists between certain cards. For example, what card did you choose?" The performer is told it was the ace of hearts. He reaches for the portion of the pack that was set aside In the beginning. This he ribbon spreads and the ace of diamonds is seen reversed in the middle. The partial deck is cut and the face-up ace brought to the top. Then the top card of the other packet is turned up: it is the ace of hearts.

"That's what I mean by sympathy—and here's how it helps me keep track of all these cards we mixed." Cards from the tops of the two piles are now turned face-up in unison, and each pair is seen to consist of mates: black sevens, black nines, red tens, and so on. Every card in the mixed packet is unaccountably matched by a corresponding card from the deck.

Method: This effect depends on the second mathematical principle found in a 1860 card trick by Charles S. Peirce, published in The Collected Papers of Charles Sanders Peirce, Vol. 4, page 473. (For further information on this trick, see "Peirce Arrow" in Volume I, pp. 397-398.) Mr. Peirce's formula has been melded here with Herbert Milton's "Sympathetic Clubs" plot, and embroidered with an unusual presentation. The trick, Mr. Elmsley points out, holds more fascination for magicians than for laymen, and is therefore better suited to performances before one's peers. Here is the working.

An arrangement must be made. Remove thirteen cards from the deck: ace through king in mixed suits. Order these cards from top to face as follows:

ace-seven-nine-t en-eight-j ack-t wo-fi vet hree-four-six-queen-king

Then remove the thirteen mates to these cards and arrange them in the same order. Turn the ace face-up on one of the two groups and insert this packet into the center of the remaining half deck. All cards, aside from the ace, should be face-down. Drop the other thirteen-card packet face-down on top of the deck. You are now ready to perform.

Introduce the effect as explained above and, as you do so, casually spread over the top thirteen cards, maintaining their order. Remove these cards from the deck and set the balance to one side.

If you wish, you can give the packet one or more straddle faros: that is, cut the top six cards from the packet and weave them into the bottom seven cards—the top and bottom cards of the bottom portion become the top and bottom cards of the shuffled packet. These faro shuffles are optional.

Explain that you wish to mix the cards in a way resembling that which would occur in a card game. Ask someone to specify the number of hands in the game. The number will normally fall within the range of two to seven. If a number higher than seven is named, point out that you have too few cards to make this practical and ask for something lower.

Deal the thirteen cards face-down into the desired number of hands. Then gather the hands. Here, the Peirce gathering formula is applied. However, Mr. Elmsley has simplified it to the following three patterns:

If two, three, four, or six hands are {iealt, assemble the piles in the order they were created: drop the first hand onto the second, these onto the third, and so on.

If seven hands are dealt, assemble the piles in reverse order, starting with the sixth pile. That is, place pile six onto five, these onto four, and so on, until all piles have been gathered but the seventh. This pile contains only one card. Drop all the gathered packets onto this card.

If five hands are dealt, use both hands at once to gather the piles. With the left hand, pick up pile three and, with the right hand, simultaneously pick up pile four. Move these two packets over the first two piles, drop pile three onto pile one, and pile four onto pile two. With the left hand, pick up the combined third and first piles, and with the right hand pick up the combined fourth and second piles. Drop the right hand's packet onto the fifth pile and the left hand's packet onto the lot.

With any of these gathering patterns, you will find that the king always becomes the top card. Double cut or slip the king to the bottom of the packet after each gather.

You may deal the packet and gather it as many times as you like, letting the audience specify the number of hands to be dealt on each round. However, two or three rounds are sufficiently convincing for most groups. To complicate matters further, you can insert straddle faros (top portion into bottom) between each round if you like. Just be certain to return the king to the face of the packet after each gathering, and to retain it there during the shuffles. Throughout the dealing mid shuffling, emphasize that the gambler must remember cards and their shifting positions. This feat will seem particularly difficult in your case, as you have not yet seen the faces of the cards.

When the last gathering of hands is made, glimpse the bottom card of the packet before you return the king to the face. Remember the value of this card. Then suggest that the exercise be complicated by having one of the cards chosen. Turn up the top card of the packet and display it. Then replace the card face-down on the packet and use its value to arrive at a seemingly random card. (The jack is counted as eleven and the queen as twelve.) The card arrived at, however, is not quite random. It will always be the ace, thanks to an attribute of the stack. Do not reverse the order of the cards as you count. Take each card under the previous one until you arrive at the desired number; then hold the face of the counted cards toward the audience, giving everyone a chance to note the ace. Drop the counted cards back onto the packet.

You will now perform one last round of dealing and gathering, and with this round you will bring the packet back to its original order. Suggest, "We'll mix the cards with one more deal—say, five hands." This time you nonchalantly nominate the number of hands. This number corresponds to the value of the card you previously glimpsed on the face of the packet. By dealing the packet into that many hands, gathering it in the manner already explained, and cutting the king from the top to the bottom, the packet will be returned to its original order: ace-seven-nlne-ten-eight~jack-two~five~three-four-six-que en-king.

All that remains is to ribbon spread the portion of the pack placed aside earlier, revealing the face-up ace in the middle. Separate the spread at the ace and gather the cards, bringing the ace and setup to the top. Set the squared deck beside the packet and turn up the ace on the packet. Lay both aces face-up in front of their piles. Then say, "That's what I mean by sympathy—and here's how it helps me keep track of all these cards we mixed."

Turn up the top cards of each packet in unison and lay them onto the aces. They are matching sevens. Continue to turn up pairs of matching cards until the smaller packet is exhausted.

There is one detail yet to be explained. What if the card you glimpse toward the finish of the mixing is an ace or has a value higher than seven? This card determines how many hands will be dealt on the last round. An ace would mean that you would simply deal the packet into a single pile, reversing its order. While this does restore the packet to the necessary sequence, it is not an acceptable procedure for this presentation. And dealing more than seven hands becomes cumbersome. Though these contingencies are covered by Peirce's original formula, nonetheless, it is best to avoid them. How? By giving the packet one or several straddle faros (top portion into bottom), until a two, three, four, five, six or seven moves into position above the king; that is, second from the face of the packet.

For the mathematically inclined, Mr. Elmsley offers a formula to calculate the position of any card in a packet of any size, after the cards have been dealt into any number of hands and gathered, following the Peirce system:

If P = the number of cards in the packet, h = the number of hands dealt, nQ = the original position of the card to be tracked, counting from any card as a reference card, Rj = the position of the card after the deal, and if h is prime to P, then—

If the cards are dealt out twice, first into hj hands, then into h2 hands, the resulting order will equal h} x h2(mod. P),

If the packet is given x faro shuffles, the order will be identical to that achieved if the cards had been dealt into h hands, where—

While Mr. Elms ley has not rigorously proven these results, they have held for all cases he has tested.

Having here treated the topic of gambling games, we will stay with the subject for one further excursion. However, sympathetic cards are swapped for sympathetic thoughts, and an entirely different method is introduced.

September 1957

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